Correction of surface roughness measurements in SPM imaging

In STM and AFM, when rough surfaces are concerned, image formation is essentially governed by the nonlinear geometrical interaction between the specimen surface and the tip surface. The shape and finite size of the tip are responsible for imperfections in images. Consequently the measured roughnesses are not exact. They are always smaller than the true roughness value because the surface is imperfectly probed. We propose a method to predict the true roughness value from the experimental image obtained. For this purpose a large variety of different 3D surfaces which mimic the experimental ones are computed and classified with respect to the shape and density of grains composing the surface. Then, by using the mathematical morphology dilation operation which describes the image formation in SPM, the corresponding dilated images are computed for different tip geometries. For each category of surfaces and given tip shapes the correction factors between the true rm.s. roughness values and the experimental ones are obtained. This allows us to predict the true roughness value.